Sheth–Tormen approximation

The Sheth–Tormen approximation extends the Press–Schechter formalism by assuming that halos are not necessarily spherical, but merely elliptical. The distribution of the density fluctuation is as follows: f(\sigma_r)=A\sqrt{\frac{2a}{\pi}}[1+(\frac{\sigma_r^2}{a\delta_c^2})^{0.3}]\frac{\delta_c}{\sigma_r}\exp(-\frac{a\delta_c^2}{2\sigma_r^2}), where \delta_c=1.686, a=0.707, and A=0.3222. The parameters were empirically obtained from the five-year release of WMAP. == Discrepancies with simulations ==

In 2010, the Bolshoi cosmological simulation predicted that the Sheth–Tormen approximation is inaccurate for the most distant objects. Specifically, the Sheth–Tormen approximation overpredicts the abundance of haloes by a factor of 10 for objects with a redshift z>10, but is accurate at low redshifts. == References ==